Microwave Sintering and Microwave Dielectric Properties of (1–x)Ca0.61La0.26TiO3-xNd(Mg0.5Ti0.5)O3 Ceramics

The (1–x)Ca0.61La0.26TiO3-xNd(Mg0.5Ti0.5)O3 [(1–x)CLT-xNMT, x = 0.35~0.60] ceramics were prepared via microwave sintering. The effects of sintering temperature and composition on the phase formation, microstructure, and microwave dielectric properties were investigated. The results show that the microwave sintering process requires a lower sintering temperature and shorter sintering time of (1–x)CLT-xNMT ceramics than conventional heating methods. All of the (1–x)CLT-xNMT ceramics possess a single perovskite structure. With the increase of x, the dielectric constant (ε) shows a downward trend; the quality factor (Qf) drops first and then rises significantly; the resonance frequency temperature coefficient (τf) keeps decreasing. With excellent microwave dielectric properties (ε = 51.3, Qf = 13,852 GHz, τf = −1.9 × 10−6/°C), the 0.65CLT-0.35NMT ceramic can be applied to the field of mobile communications.


Introduction
With the advent of the 5G era, microwave dielectric ceramics attract more and more attention [1]. Microwave dielectric ceramics can not only be used as insulating substrates material in microwave circuits, also as the key basic material to fabricate dielectric resonators, dielectric filters, dielectric oscillators, phase shifters, microwave capacitors, etc., for microwave communication technology [2]. Therefore, microwave components play an increasingly important role in miniaturization, integration, and cost reduction of modern communication tools [3]. The dielectric materials with high dielectric constant, high Qf value, near-zero temperature coefficient of resonance frequency, and low sintering temperature are strong candidates for 5G technology [4].
The Ca 0.61 La 0.26 TiO 3 (CLT) ceramic, with typical perovskite structure, is characterized by a high dielectric constant (ε = 120) and a high quality factor (Qf = 10,700 GHz), but a very high positive resonant frequency temperature coefficient (τ f = 304 × 10 −6 / • C) [5]. The Nd(Mg 0.5 Ti 0.5 )O 3 (NMT) ceramic also has a perovskite structure with Qf value of 36,900~151,000 GHz, the ε value is only 25~26, and the τ f is a large negative value (−72 × 10 −6~− 47 × 10 −6 / • C) [6,7]. The microwave dielectric ceramics with moderate ε, high Qf, and τ f of close to zero can be obtained, by combining Ca 0.8 Sr 0.2 TiO 3 or CLT with NMT ceramics [8,9]. However, preparing the CLT-NMT dielectric ceramics by conventional sintering requires excessively high sintering temperature and long sintering time (1650 • C, 3 h; according to our previous work). A small amount of CuO, ZnO and other sintering aids can be added to reduce the sintering temperature [10,11], but it is difficult to avoid the introduction of the second phase and reduction of the microwave dielectric properties.
As an efficient sintering method for materials, microwave sintering can effectively reduce the sintering temperature, increase the sintering rate, and promote the grain re- where f 1 and f 2 represent the resonant frequency at T 1 (25 • C) and T 2 (85 • C), respectively.

Sintering Characteristics
The influence of sintering temperature on the density (ρ) of (1−x)CLT-xNMT ceramics is shown in Figure 1. With the increase of sintering temperature (T), the ρ presents the tendency of increasing first. However, with the further increase of T, the ρ tends to decrease. It may be attributed to oversintering.
The relationship between the ρ and relative density (ρ r ) of the (1−x)CLT-xNMT ceramic with x is shown in Figure 2. It can be seen intuitively that the ρ increases with the increase of x, up to 5.457 (x = 0.60), mainly because the density of NMT ceramic (6.16 g/cm 3 ) is higher than that of CLT ceramic (4.51 g/cm 3 ). The ρ r is all higher 95.5% with slightly floating and reaches 96.9% when x = 0.50. The relationship between the ρ and relative density (ρr) of the (1−x)CLT-xNMT ceramic with x is shown in Figure 2. It can be seen intuitively that the ρ increases with the increase of x, up to 5.457 (x = 0.60), mainly because the density of NMT ceramic (6.16 g/cm 3 ) is higher than that of CLT ceramic (4.51 g/cm 3 ). The ρr is all higher 95.5% with slightly floating and reaches 96.9% when x = 0.50.

Phase and Microstructure
The XRD patterns of the (1−x)CLT-xNMT ceramics are illustrated in Figure 3. The diffraction peak positions are almost completely overlapped in the composition range of x = 0.35~0.60, indicating a perovskite structure without second phase. It should be pointed out that superlattice diffraction peaks were observed when x = 0.40 and 0.45. The enlarged part of 32.1~33.3°, as shown in the upper right corner of Figure 3, indicates that the main diffraction peaks of (1−x)CLT-xNMT ceramics shift toward low angle with the increase of x. It suggests the increasing lattice constant of the identified perovskite structure.  The relationship between the ρ and relative density (ρr) of the (1−x)CLT-xNMT ceramic with x is shown in Figure 2. It can be seen intuitively that the ρ increases with the increase of x, up to 5.457 (x = 0.60), mainly because the density of NMT ceramic (6.16 g/cm 3 ) is higher than that of CLT ceramic (4.51 g/cm 3 ). The ρr is all higher 95.5% with slightly floating and reaches 96.9% when x = 0.50.

Phase and Microstructure
The XRD patterns of the (1−x)CLT-xNMT ceramics are illustrated in Figure 3. The diffraction peak positions are almost completely overlapped in the composition range of x = 0.35~0.60, indicating a perovskite structure without second phase. It should be pointed out that superlattice diffraction peaks were observed when x = 0.40 and 0.45. The enlarged part of 32.1~33.3°, as shown in the upper right corner of Figure 3, indicates that the main diffraction peaks of (1−x)CLT-xNMT ceramics shift toward low angle with the increase of x. It suggests the increasing lattice constant of the identified perovskite structure.

Phase and Microstructure
The XRD patterns of the (1−x)CLT-xNMT ceramics are illustrated in Figure 3 The lattice constant (a, b, c) and unit cell volume (Vu) of (1−x)CLT-xNMT ceramics are shown in Figure 4. Both lattice constant and unit cell volume gradually increase with the increasing x, which is in accordance with the XRD analysis. This trend depends on two factors: the decreasing vacancy concentration in A-site, the increasing Mg 2+ content  The lattice constant (a, b, c) and unit cell volume (V u ) of (1−x)CLT-xNMT ceramics are shown in Figure 4. Both lattice constant and unit cell volume gradually increase with the increasing x, which is in accordance with the XRD analysis. This trend depends on two factors: the decreasing vacancy concentration in A-site, the increasing Mg 2+ content (r(Mg 2+ ) > r(Ti 4+ ), r(Mg 2+ ) = 0.072 nm, r(Ti 4+ ) = 0.061 nm when CN = 6) in B-site [14], with the increase of NMT content in (1−x)CLT-xNMT ceramics. The lattice constant (a, b, c) and unit cell volume (Vu) of (1−x)CLT-xNMT ceramics are shown in Figure 4. Both lattice constant and unit cell volume gradually increase with the increasing x, which is in accordance with the XRD analysis. This trend depends on two factors: the decreasing vacancy concentration in A-site, the increasing Mg 2+ content (r(Mg 2+ ) > r(Ti 4+ ), r(Mg 2+ ) = 0.072 nm, r(Ti 4+ ) = 0.061 nm when CN = 6) in B-site [14], with the increase of NMT content in (1−x)CLT-xNMT ceramics. . When x ≤ 0.55, the grain size (10~30 μm) is relatively uniform and change slightly with the increase of NMT content. When x = 0.60, the grain size (20~50 μm) is significantly larger than that of the rest composition. When x < 0.60, strip-shaped grains can be observed, which is similar to the CaTiO3-La(Mg0.5Ti0.5) ceramics [15].  Figure 5. When x ≤ 0.55, the grain size (10~30 µm) is relatively uniform and change slightly with the increase of NMT content. When x = 0.60, the grain size (20~50 µm) is significantly larger than that of the rest composition. When x < 0.60, strip-shaped grains can be observed, which is similar to the CaTiO 3 -La(Mg 0.5 Ti 0.5 ) ceramics [15].

Microwave Dielectric Properties
The relationship between dielectric constant (ε) and composition of the (1-x)CLT-xNMT ceramics is illustrated in Figure 6. With the increase of x, the ε gradually decreases from 51.3 to 36.4 because the ε of NMT (~24) is much lower than that of CLT (~120). To evaluate the influence of porosity (p) on the ε, the theoretical dielectric constant (εth) of (1x)CLT-xNMT ceramics can be calculated according to the following equation [16,17]:

Microwave Dielectric Properties
The relationship between dielectric constant (ε) and composition of the (1-x)CLT-xNMT ceramics is illustrated in Figure 6. With the increase of x, the ε gradually decreases from 51.3 to 36.4 because the ε of NMT (~24) is much lower than that of CLT (~120). To evaluate the influence of porosity (p) on the ε, the theoretical dielectric constant (ε th ) of (1-x)CLT-xNMT ceramics can be calculated according to the following equation [16,17]: where ε th is the dielectric constant of a theoretically fully dense ceramic, ε is the measured dielectric constant, p is the porosity (p = 100%-ρ r ). Furthermore, Equation (2) can be simplified as follows due to ε >> 1: Materials 2021, 14, x FOR PEER REVIEW 6 of 9 As shown in Figure 6, the εth of (1-x)CLT-xNMT ceramics decreases from 54.2 to 38.3 with the increase of x. It indicates an improvement space of 4.9~6.4%. The Qf value of the (1−x)CLT-xNMT ceramics is presented in Figure 7. It ascends from 13,852 GHz (x = 0.35) to 17,148 GHz (x = 0.40) and then drops to 8482 GHz (x = 0.45) and finally climbs to 32,637 GHz (x = 0.60). Generally, the appearance of superlattice diffraction peaks is related to the 1:1 ordering of Mg 2+ and Ti 4+ [15], which often affects the dielectric loss and then Qf. The dielectric loss decreases with increasing of ions' degree of order, but increases with attenuation of ions' phonon mode. As x increases to 0.40, the ions' degree of order constantly deepens and the phonon mode attenuates slightly, which results in an increase of Qf. When x climbs to 0.45, the ions' degree of order continues to deepen, but the phonon mode attenuates intensively, which leads to a decrease in Qf. Later, the further increase of x transforms the (1−x)CLT-xNMT ceramics from a CLT-based ordered solid solution to an NMT-based ordered solid solution, decreasing dielectric loss, and increasing the Qf value to 32,637 GHz (x = 0.60). As shown in Figure 6, the ε th of (1-x)CLT-xNMT ceramics decreases from 54.2 to 38.3 with the increase of x. It indicates an improvement space of 4.9~6.4%.
The Qf value of the (1−x)CLT-xNMT ceramics is presented in Figure 7. It ascends from 13,852 GHz (x = 0.35) to 17,148 GHz (x = 0.40) and then drops to 8482 GHz (x = 0.45) and finally climbs to 32,637 GHz (x = 0.60). Generally, the appearance of superlattice diffraction peaks is related to the 1:1 ordering of Mg 2+ and Ti 4+ [15], which often affects the dielectric loss and then Qf. The dielectric loss decreases with increasing of ions' degree of order, but increases with attenuation of ions' phonon mode. As x increases to 0.40, the ions' degree of order constantly deepens and the phonon mode attenuates slightly, which results in an increase of Qf. When x climbs to 0.45, the ions' degree of order continues to deepen, but the phonon mode attenuates intensively, which leads to a decrease in Qf. Later, the further increase of x transforms the (1−x)CLT-xNMT ceramics from a CLT-based ordered solid solution to an NMT-based ordered solid solution, decreasing dielectric loss, and increasing the Qf value to 32,637 GHz (x = 0.60).
order, but increases with attenuation of ions' phonon mode. As x increases to 0.40, the ions' degree of order constantly deepens and the phonon mode attenuates slightly, which results in an increase of Qf. When x climbs to 0.45, the ions' degree of order continues to deepen, but the phonon mode attenuates intensively, which leads to a decrease in Qf. Later, the further increase of x transforms the (1−x)CLT-xNMT ceramics from a CLT-based ordered solid solution to an NMT-based ordered solid solution, decreasing dielectric loss, and increasing the Qf value to 32,637 GHz (x = 0.60). Similarly, the effect of porosity (p) on the Qf value (with 10 3~1 0 4 GHz order of magnitude) can be evaluated by the following equation [18]: where Q0 is the intrinsic quality factor, and p is the porosity. The results suggest that an improvement space of 503~1741 GHz. Similarly, the effect of porosity (p) on the Qf value (with 10 3~1 0 4 GHz order of magnitude) can be evaluated by the following equation [18]: where Q 0 is the intrinsic quality factor, and p is the porosity. The results suggest that an improvement space of 503~1741 GHz. The temperature coefficient of resonance frequency (τ f ) and tolerance factor (t) of the (1−x)CLT-xNMT ceramics are shown in Figure 8. The relationship between the τ f and temperature coefficient of dielectric constant (τ ε ) and linear expansion coefficient (α L ) can be identified as follows [19,20]: where the α L of ceramics is 6~10 × 10 −6 / • C [21]. Therefore, the value of the τ f depends on the τ ε .
Materials 2021, 14, x FOR PEER REVIEW 7 of 9 The temperature coefficient of resonance frequency (τf) and tolerance factor (t) of the (1−x)CLT-xNMT ceramics are shown in Figure 8. The relationship between the τf and temperature coefficient of dielectric constant (τε) and linear expansion coefficient (αL) can be identified as follows [19,20]: where the αL of ceramics is 6~10 × 10 −6 /°C [21]. Therefore, the value of the τf depends on the τε. In 1926, Goldschmidt [22] initially proposed the tolerance factor (t) to evaluate the stability of crystal structure. As to perovskite structure (ABO3), the t can be calculated according to the following equation [23]: where RA, RB and RO are the radius of A-site ions, B-site ions and O 2− , respectively. The effective ionic radius from Shannon [14] were used to calculate the t of (1−x)CLT-xNMT ceramics. Generally, the t of the perovskite structure should be in the range of 0.77~1.1 and the closer to 1 t is, the stabler the perovskite structure is. Colla et al. [21] studied the relationship between the tilt of BO6 octahedron in ABO3type perovskite lattice and the temperature coefficient of dielectric constant (τε). The re- In 1926, Goldschmidt [22] initially proposed the tolerance factor (t) to evaluate the stability of crystal structure. As to perovskite structure (ABO 3 ), the t can be calculated according to the following equation [23]: where R A, R B and R O are the radius of A-site ions, B-site ions and O 2− , respectively. The effective ionic radius from Shannon [14] were used to calculate the t of (1−x)CLT-xNMT ceramics. Generally, the t of the perovskite structure should be in the range of 0.77~1.1 and the closer to 1 t is, the stabler the perovskite structure is. Colla et al. [21] studied the relationship between the tilt of BO 6 octahedron in ABO 3type perovskite lattice and the temperature coefficient of dielectric constant (τ ε ). The results show that the τ ε is mainly affected by the tilt of BO 6 octahedron. The increasing tilt of BO 6 octahedron will result in the change of the τ ε to the positive direction. The tilt degree of BO 6 octahedron can be described by the t: greater difference between the t value and 1 means greater tilt degree [23]. The τ ε and the t have the following regularity: when t < 0.965, the decrease of t will lead to the change of τ ε to the positive direction. For the (1−x)CLT-xNMT ceramics, the decrease of t value will lead to the increasing tilt degree of the BO 6 octahedron. Thus the τ ε will increase and the τ f will decrease to the negative direction, as shown in Figure 8.

Conclusions
The (1-x)Ca 0.61 La 0.26 TiO 3 -xNd(Mg 0.5 Ti 0.5 )O 3 [x = 0.35~0.60, (1-x)CLT-xNMT] ceramics were prepared by microwave sintering. The effects of sintering process and component distribution compare on its phase composition, microstructure, and microwave dielectric properties were investigated. Microwave sintering can effectively reduce the sintering temperature and the sintering time. The (1-x)CLT-xNMT ceramics have formed a perovskite structure. As x increases, the ε shows a downward trend, the Qf first drops to 8482 GHz and then rises to 32,637 GHz, and the τ f keeps decreasing. When x = 0.35, the comprehensive microwave dielectric performance is: ε = 51.3, Qf = 13,852 GHz, τ f = −1.9 × 10 −6 / • C (1550 • C, 30 min). The (1-x)CLT-xNMT ceramics can be applied to the field of mobile communications.